Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include"bits/stdc++.h"
using namespace std;
#define D 100000000
int main() {
	double a[1001], b[1001], c[2],min1=D,min2=D;
	int n,i2=0,i3=0;
	memset(a, 0, sizeof(a));
	memset(b, 0, sizeof(b));
	memset(c, 0, sizeof(c));
	cin >> n;
	for (int i = 0; i < n; i++)cin >> a[i];
	sort(a, a + n);
	for (int i = 1; i < n - 2; i++) {
		if (a[i] - a[i - 1] < min1) {
			min1 = a[i] - a[i - 1];
		}
	}
	for (int i = 1; i < n ; i++) {
		if (a[i] - a[i - 1] < min2) {
			min2 = a[i] - a[i - 1];
			b[i2] = 0; b[i3] = 0;
			i2 = i;
			i3 = i - 1;
			b[i2] = 1; b[i3] = 1;
		}
	}
	//cout << "kita" << endl;
	int j = 0;
	for (int i = n-1; i >-1; i--) {
		if (j == 2)break;
		if (b[i] == 0) {
			c[j] = a[i];
			j++;
		}
	}
	double SUM = max((a[n - 1] + a[n - 2]) / (double)min1, (c[0]+c[1])/ (double)min2);
	printf("%.5f\n", SUM);
}